Sami Mohamad El Smaili
The emergence of concepts such as the internet of things (IoT) is but a manifestation of the increasing integration of communication and data acquisition systems in a wide range of devices and in a plethora of applications. Pushing the limits of traditional Nyquist-based systems, such widespread integration of acquisition systems is coupled with the increasing demand for lower power, higher bandwidth, multi-standard and reconfigurable systems. Compressive sensing promises to alleviate much of the constraints facing Nyquist-based systems and provide efficient solutions in all these areas. However, the current approaches for implementing compressive sensing suffer from several limitations:
- A gap between theory and application: reconstruction algorithms use an ideal model of the system that the hardware is designed to mimic. However, in most cases, the ideal model might not be the only one that guarantees reconstruction accuracy, which results in an unduly constrained design. In fact, the theory frames the condition for successful reconstruction in terms of the very general concept of restricted isometry property (RIP) that can be applied to any system model. The ideality of the ideal model does not necessarily has its roots originating in the theory; a more practical model that is easier to mimic can still satisfy the RIP and be considered ideal.
- General and widely used architectures have as parameters the number of acquired measurements and signal sparsity. Because these parameters are defined by the application rather than designed, there is little room to tweak the design, at the system level, to manage various system trade-offs and to overcome practical challenges such as the resetting frequency of an integrator or the window length in each projection channel.
- Applicability to realms beyond that of sparse signals: In many communication applications, signals are not sparse (and should not be for bandwidth utilization), but random acquisition architecture can still provide tremendous benefits and provide novel solutions. Reaping the benefits of random acquisition in such domains requires new architectures that go beyond the traditional application scope of compressive sensing.
The work we propose as part of this thesis aims at overcoming these limitations and expanding the realm of compressive sensing into new areas and applications. In this work we
- Provide a practical approach to compressive sensing that starts from a practical system model to derive system requirements for successful reconstruction. We consider the basic building block of compressive sensing, the projection channel, and assume a general filter is used rather than an integrator (the ideal model). We derive the conditions that such a model should have to satisfy the restricted isometry property and show that the new requirements are far less restrictive and more practical than traditional requirements stemming from an integrator-based model.
- Develop an approach for quantifying hardware variability and model uncertainty and its effect on reconstruction accuracy. Particularly, we study the effect of filter pole variability on reconstruction, which might be due to model approximations or hardware variability.
- Propose a multi-channel random demodulator that bridges the gap between the two main architectures, the random demodulator consisting of one projection channel, and the random modulator pre integrator, which uses M channels for M measurements. The multi-channel random demodulator has the number of channels as a design parameter, which can be used to manage practical trade-offs such as the integrator reset frequency and the window length in each channel. We utilize this architecture in the reconfigurable receiver architecture that we also present in this work.
- Develop a framework for random acquisition reconfigurable receivers, which expands the realm of compressive sensing to communication systems where signals are dense but their supports are known. We develop a design methodology for such systems, linking the various system parameters to system metrics.
- Propose and analyze an ADC-less architecture for sensors that breaks from the conventional compressive sensing approach of digitizing measurements at the acquisition site. We study when this approach is more beneficial than the traditional approach of digitizing on the acquisition site.